Hi @jayg001 : There are a few things that come in to play here. In no particular order:

1. Sample Size:

-For small sample sizes, it is less likely that you will reject a plausible distribution via some Goodness-of-Fit test even when

the distribution is not correct (i.e., low power). This results in accepting the wrong distribution.

-Conversely, for large sample sizes you may reject a distribution because it is overpowered. i.e., even negligible, departures

from the distribution being tested will result in rejecting the distribution. This results in rejecting a distribution that is, for all

intents and purposes, adequate.

2. We never really know if the distribution is Normal, or SHASH, or any other distribution. The Good-of-Fit test may not reject a

given distribution, but that doesn't prove the distribution is correct; it only means that there is not sufficient evidence to reject it.

It's like how the assumption or innocence is applied in a trial. "Not guilty" does not mean innocent. Not guilty means there was

not enough evidence to convict...

3. A transformation can change how much influence an individual point(s) has on Goodness-of-Fit tests.

FWIW Edit: Generally speaking, I'm not a big fan of Goodness-of-Fit tests (see above for why). I tend to look at QQ plots etc.

These are my initial thoughts. I hope they are helpful.